Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

TL;DR

This paper introduces a stable, improvable quantum Monte Carlo method for calculating excited-state energies in large active spaces, achieving high accuracy comparable to state-of-the-art techniques.

Contribution

The authors develop a novel asymmetric subspace iteration approach within FCI-FRI that avoids dot products of random vectors, enabling efficient excited-state calculations in large strongly correlated systems.

Findings

Accurately computes excited-state energies in large active spaces.

Achieves agreement within sub-milliHartree with existing methods.

Estimates excitation energies within about 0.1 eV.

Abstract

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of strongly correlated molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods -- including heat-bath CI, the density matrix renormalization group approach, and FCIQMC -- to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.